Algebraic topology book after John Lee "Introduction to topological manifolds"

Question

What algebraic topology book do you suggest to study after one has studied John Lee's "Introduction to topological manifolds"?

Answer 1

I also recently finished Lee's book (although I don't believe one can ever "finish" a math textbook) and I'm finding J.P May's A Concise Course in Algebraic Topology very illuminating
(it's also available for free on his website which is nice).

When I have trouble understanding some passages or I find the motivation for some things lacking (since May's book is indeed quite concise) I usually consult Hatcher who Is significantly more wordy (in my opinion) and is, as I understand it, the standard reference for algebraic topology
(+ his book can also be found for free on his website). \

I've also found Pierre Schapira's Lecture notes helpful. He is, like May, a bit heavier on the use of categorical terminology (although I haven't read much thus far, but the little I did get around to read seemed great).

Hope this helps :)

Answer 2

I'm not familiar with Lee's book. But if you're ready I know a really good, thorough, algebraic topology book is the one by Spanier. I had the pleasure to take one of his courses. Boy was he good.

Munkres and Greenburg and Harper are also both good.